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Math Help - Using the good old Mean Value Theorem

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    Using the good old Mean Value Theorem

    Use the MVT to prove that |sin(x) - sin(y)|\leq|x-y| for all x,y\in\mathbb{R}
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    Use the fact that l cos(x)l  \leq 1  \forall x
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Kipster1203 View Post
    Use the MVT to prove that |sin(x) - sin(y)|\leq|x-y| for all x,y\in\mathbb{R}
    And that |\sin(x)-\sin(y)|\leqslant|x-y|\Leftrightarrow\left|\frac{\sin(x)-\sin(y)}{x-y}\right|\leqslant 1
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